Interpolation: Summary & Update

2023-12-06

Inverse Distance Weighting

Spatial interpolation that calculates cell values (\(V\)) based on a weighted average of sample points.
The weights are inversely proportional to the distance between the predicted and sampled locations.
- This means points further away have less influence on the predicted value.
Predicted value \(V\) is calculated as \[ V = \frac{\sum_{i=1}^n v_i \frac{1}{d_i^p}} {\sum_{i=1}^n \frac{1}{d_i^p}} \] where \(d\) is the distance between prediction and measurement points, \(v_i\) is the measured parameter value, and \(p\) is a power parameter.
Well-known method
Considered among the most “simple” spatial interpolation methods
Output is sensitive to clustering
Does not provide standard errors
Typically use training/test datasets to evaluate “goodness of fit”

Modified from ArcGIS Pro

\(p\) controls the significance of the known points based on their distance from the predicted point.
As \(p\) increases, the interpolated values approach the value of the nearest sample point.
Default value is typically 2, although no mathematical or practical reason for this.

Precipitation data from Texas:

[21 stations]

[inverse distance weighted interpolation]

[inverse distance weighted interpolation]

Map of Nova Scotia with “measured” superchill likelihood. (Gold buffer is 2 km from the coast)

We want to interpolate AROUND the province, not THROUGH it!!

Training points (black) and test points (red).

Note that only point is selected per grid box (so some stations are left out).

With training dataset:

Better understand the paths created.
Determine if can use all stations or if choosing 1 station per grid addresses the clustering issue.
Set up cross-validation (n-fold or k-fold).
Compare to regular IDW.
Figure out mapping + colour scale.
Repeat for heat stress.